# 210+ Discrete Structure (DS) Solved MCQs

Chapters

34
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Chapter: Unit 1
1.

A. 1
B. 2
C. 3
D. 4
2.

## Let A={2,{4,5},4} Which statement is correct?

A. 5 is an element of A.
B. {5} is an element of A.
C. {4, 5} is an element of A.
D. {5} is a subset of A.
Answer» C. {4, 5} is an element of A.
3.

## Which of these sets is finite?

A. {x | x is even}
B. ) {1, 2, 3,...}
C. {1, 2, 3,...,999,1000}
D. none
4.

## Which of these sets is not a null set?

A. A = {x | 6x = 24 and 3x = 1}
B. B = {x | x + 10 = 10}
C. C = {x | x is a man older than 200 years}
D. D = {x | x < x}
Answer» B. B = {x | x + 10 = 10}
5.

A. 3
B. 6
C. 8
D. 4
6.

## . Which set S does the power set 2S = {Ф,{1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}} come from?

A. {{1},{2},{3}}
B. {1, 2, 3}
C. {{1, 2}, {2, 3}, {1, 3}}
D. {{1, 2, 3}}
7.

## Let A = {x, y, z}, B = {v, w, x}. Which of the following statements is correct?

A. A U B ={v, w, x, y, z}
B. A U B = {v, w, y, z}
C. A U B = {v, w, x, y}
D. A U B ={x, w, x, y, z}
Answer» A. A U B ={v, w, x, y, z}
8.

A. 1 and 2
B. 2 and 3
C. 1 and 3
D. all are equal
9.

## A U A=A according to …….law

A. Associative law
B. commutative law
C. Indempotent law
D. distributive law
10.

A. union
B. intersection
C. universal
D. cardinal
11.

A. TRUE
B. FALSE
C. Both
D. None
12.

A. TRUE
B. FALSE
C. Both
D. None
13.

A. TRUE
B. FALSE
C. Both
D. None
14.

A. TRUE
B. FALSE
C. Both
D. None
15.

A. TRUE
B. FALSE
C. Both
D. None
16.

## one of the A or B is uncountably infinite and one is countably infinite then | AUB| will be

A. countably infinite
B. uncountably finite
C. countably finite
D. uncountably infinite
17.

A. n(n+1)
B. n
C. n(n+1)0.5
D. n(n+2)
18.

## Let P(S) denote the power set of set S. which of the is always true

A. P(P(s))=p(s)
B. P(S)∩ S= P(S)
C. P(S)∩P(P(S)) ={Ф}
D. None
19.

A. TRUE
B. FALSE
C. Both
D. None
20.

A. 100
B. 25
C. 56
D. 20
21.

A. Multiset
B. ordered set
C. set
D. None
22.

A. 9
B. 8
C. 7
D. 6
23.

## If U = {1, 2, 3, . . . 10 } and S = { 4, 5, 6, 7, 8 }, then S ' =

A. { 9, 10 }
B. {1, 2, 3 }
C. {1, 2, 3 9 }
D. {1, 2, 3 9 10 }
Answer» D. {1, 2, 3 9 10 }
24.

## If U = {1, 2, 3, . . . 20 } and S = set of prime numbers , then S =

A. { 3, 5, 7, 11, 13, 17 }
B. { 2, 3, 5, 7, 11, 13, 17, 19 }
C. {1, 3, 5, 7, 9, 11, 13, 15, 17, 19 }
D. {1, 2, 3, 5, 7, 11, 13, 17 }
Answer» B. { 2, 3, 5, 7, 11, 13, 17, 19 }
25.

## Consider the statement,“If n is divisible by 30 then n is divisible by 2 and by 3 and by 5.”Which of the following statements is equivalent to this statement?

A. If n is not divisible by 30 then n is divisible by 2 or divisible by 3 or divisible by 5
B. If n is not divisible by 30 then n is not divisible by 2 or not divisible by 3 or not divisible by 5
C. If n is divisible by 2 and divisible by 3 and divisible by 5 then n is divisible by 30.
D. If n is not divisible by 2 or not divisible by 3 or not divisible by 5 then n is not divisible by 30
Answer» D. If n is not divisible by 2 or not divisible by 3 or not divisible by 5 then n is not divisible by 30
26.

## Which of the following statements is the contrapositive of the statement, “You win the game if you know the rules but are not overconfident.”

A. If you lose the game then you don’t know the rules or you are overconfident.
B. A sufficient condition that you win the game is that you know the rules or you are not over confident
C. If you don’t know the rules or are overconfident you lose the game.
D. If you know the rules and are overconfiden t then you win the game.
Answer» A. If you lose the game then you don’t know the rules or you are overconfident.
27.

## A sufficient condition that a triangle T be a right triangle is that a2 + b2 = c2. An equivalent statement is

A. If T is a right triangle then a2 + b2 = c2.
B. If a2 + b2 = c2 then T is a right triangle.
C. If a2 + b2 6= c2 then T is not a right triangle.
D. T is a right triangle only if a2 + b2 = c2.
Answer» B. If a2 + b2 = c2 then T is a right triangle.
28.

## Which of the following is the inverse of the statement: " If I eat a mango than I do not drink milk".

A. I drink milk only if I do not eat a mango
B. If I don’t eat a mango then I drink milk
C. If I do not drink milk then I eat mango
D. None
Answer» B. If I don’t eat a mango then I drink milk
29.

## If p= It is hot, and q= It is sultry, which of the following sentences in the appropriate version for the symbolic expression: -p٨ q

A. If it is sultry then it is hot
B. It is sultry only if it is hot
C. It is sultry and it is not hot
D. None
30.

## which of the following is the contrapositive of the statement: " A quadrilateral is a square only if it is both rectangle and a rhombus".

A. If a rectangle is not a a rhombus it is not a square
B. If a rhombus is not rectangle it is not a square
C. If a quadrilateral is neither a rectangle nor a rhombus then it is not a square
D. None
Answer» C. If a quadrilateral is neither a rectangle nor a rhombus then it is not a square
31.

## For a conditional statement p===>q, which of the following is incorrect.

A. Converse of the inverse is its contrapositive
B. contrapositive of the converse is its inverse
C. Inverse of the contrapositiv e is its converse
D. None
32.

A. ~xp٨q
B. pV~q
C. ~xpVq
D. pV~q
33.

A. ~xp٨q
B. pV~q
C. ~xpVq
D. pV~q
34.

A. ~xp٨q
B. pV~q
C. ~xpVq
D. pV~q
35.

## the truth table for exclusive disjunction will be

A. tautology
C. Logical equivalent
D. p or q but not both
Answer» D. p or q but not both
36.

## The conditional statement p→q and its contrapositive are….

A. Converse
B. Inverse
C. Logically equivalent
D. None
37.

A. 3
B. 6
C. 9
D. None
38.

A. 6
B. 9
C. 18
D. None
39.

A. P
B. U-P
C. U-Q
D. Ф
40.

A. 16
B. 15
C. 10
D. 12
41.

A. A
B. B
C. C
D. D
42.

A. A
B. B
C. C
D. D
43.

A. A
B. B
C. C
D. D
44.

A. A
B. B
C. C
D. D
45.

A. A
B. B
C. C
D. D
46.

## Which of the following sets are equal. 1. {p,q,m,n} 2.{m,p,n,q} 3.{q,p,p,m,m,p,n} 4.{p,q,n,,n,m}

A. 1 and 2 are equal
B. 2 and 3 are equal
C. 3 and 4 are equal
D. All are equal.
47.

## Consider the set A={{1,3,5},{7,9,11},{13,15}} then determine which of the following is/are true. 1.1ЄA 2.{{1,3,5}} CA 3. Ф subet of A 4. A

A. 2 and 3 is true
B. 1 and 3 is true
C. 3 is true
D. None
Answer» A. 2 and 3 is true
48.

A. Valid
B. Not valid
C. Both a and b
D. None
49.

A. 30
B. 52
C. 40
D. 68
50.

A. 30
B. 52
C. 40
D. 68
51.

A. 73
B. 72
C. 50
D. 54
52.

A. 52
B. 54
C. 60
D. 25
53.

A. 54
B. 12
C. 7
D. 8
54.

A. TRUE
B. FALSE
C. none
D. both a and b
55.

A. Tautology
C. Negation
D. Sentence
56.

A. Tautology
C. Negation
D. Sentence
57.

## p→q is logically equivalent to ~p V q according to…

A. Identity law
B. Implication law
C. associative law
D. Absoption law
58.

## A logical expression which consist of a product of elementary sum is caleed…..

A. Disjunctive normal form
B. Conjunctive normal form
C. Normal form
D. None
59.

## A logical expression which consist of a sum of product is caleed…..

A. Disjunctive normal form
B. Conjunctive normal form
C. Normal form
D. None
60.

A. CNF
B. DNF
C. Predicates
D. Quantifiers
61.

A. Valid
B. Invalid
C. Both a and b
D. none
62.

B. Tautology
C. predicate
D. None
63.

A. Valid
B. Invalid
C. Both a and b
D. none
64.

A. TRUE
B. FALSE
C. both a and b
D. none
65.

A. TRUE
B. FALSE
C. both a and b
D. none
66.

A. 250
B. 550
C. 120
D. 140
67.

A. p Vq
B. (p٨q) Vr
C. p ٨r
D. (p Vq) Vr
68.

A. 10
B. 12
C. 35
D. 9
69.

A. 54
B. 16
C. 10
D. 35
70.

A. 6
B. 16
C. 7
D. 10
71.

A. 22
B. 45
C. 42
D. 14
72.

A. Satisfiable
B. tautology
C. unsatisfiable
73.

## If P and Q stands for the statement P : It is hot Q : It is humid, then what does the following mean? P Ù (~ Q):

A. It is got and it is humid
B. It is hot and it is not humid
C. it is not hot and it is humid
D. none
Answer» B. It is hot and it is not humid
74.

A. 10
B. 9
C. 8
D. 7
75.

A. absurdity
C. tautology
D. none
76.

## Let p be “He is tall” and let q “He is handsome”. Then the statement “It is false that he is short or handsome” is:

A. p ^ q
B. ~ (~ p ^q)
C. p^ ~ q
D. ~ p ^q
Answer» B. ~ (~ p ^q)
77.

## Let P(S) denotes the powerset of set S. Which of the following is always true?

A. P(P(S)) = P(S)
B. P(S) IS = P(S)
C. P(S) I P(P(S)) = {ø}
D. S € P(S)
78.

A. (p v q)→p
B. p v (q→p)
C. p v (p→q)
D. p→(p→q)
79.

## Which of the following statement is the negation of the statement “4 is even or -5 is negative”?

A. 4 is odd and -5 is not negative
B. 4 is even or -5 is not negative
C. 4 is odd or -5 is not negative
D. 4 is even and -5 is not negative
Answer» A. 4 is odd and -5 is not negative
80.

A. p → q
B. ~p →~q
C. ~q→~p
D. None
81.

A. Invalid
B. Valid
C. Both a and b
D. None
82.

A. TRUE
B. FALSE
C. Both a and b
D. None
83.

A. TRUE
B. FALSE
C. Both a and b
D. None
84.

A. absurdity
C. tautology
D. none
85.

## Represent statement into predicate calculus forms : "Not all birds can fly". Let us assume the following predicates bird(x): “x is bird” fly(x): “x can fly”.

A. ∃x bird(x) V fly(x)
B. ∃x bird(x) ^ ~ fly(x)
C. ∃x bird(x) ^ fly(x)
D. None
Answer» B. ∃x bird(x) ^ ~ fly(x)
86.

## Represent statement into predicate calculus forms : "If x is a man, then x is a giant." Let us assume the following predicates man(x): “x is Man” giant(x): “x is giant”.

A. ∀ (man(x)→ ~giant(x))
B. ∀ man(x)→ giant(x)
C. ∀ (man(x)→ giant(x))
D. None
87.

## Represent statement into predicate calculus forms : "Some men are not giants." Let us assume the following predicates man(x): “x is Man” giant(x): “x is giant”.

A. ∃x man(x) ^ giant(x)
B. ∃x man(x) ^ ~ giant(x)
C. ∃x man(x) V ~ giant(x)
D. None
Answer» B. ∃x man(x) ^ ~ giant(x)
88.

## Represent statement into predicate calculus forms : There is a student who likes mathematics but not history. Let us assume the following predicates student(x): “x is student.” likes(x, y): “x likes y”. and ~likes(x, y) “x does not like y”.

A. ∃x [student(x) ^ likes(x, mathematics) ^~ likes(x, history)]Q.
B. ∃x [student(x) ^Vlikes(x, mathematics) V~ likes(x, history)]Q.
C. ∃x [student(x) ^ ~likes(x, mathematics) ^likes(x, history)]Q.
D. None
Answer» A. ∃x [student(x) ^ likes(x, mathematics) ^~ likes(x, history)]Q.
89.

A. FALSE
B. TRUE
C. Both a and b
D. None
90.

A. absurdity
C. tautology
D. none
91.

A. FALSE
B. TRUE
C. Both a and b
D. None
92.

A. FALSE
B. TRUE
C. Both a and b
D. None
93.

A. Invalid
B. Valid
C. Both a and b
D. None
94.

A. 78
B. 98
C. 23
D. 43
95.

A. 10
B. 8
C. 9
D. 4
96.

A. absurdity
C. tautology
D. none
97.

## Write the negation in good english sentence : "Jack did not eat fat, but he did eat broccoli."

A. If Jack eat and broccoli then he did ate fat.
B. If Jack did not eat broccoli then he did ate fat.
C. If Jack did not eat broccoli or he did ate fat.
D. If Jack did not eat broccoli then he did not ate fat.
Answer» B. If Jack did not eat broccoli then he did ate fat.
98.

## Write the negation in good english sentence : The weather is bad and I will not go to work.

A. The weather is not bad or I will go to work.
B. The weather is good or I will go to work.
C. The weather is not bad or I will not go to work.
D. None
Answer» A. The weather is not bad or I will go to work.
99.

## Write the negation in good english sentence : Mary lost her lamb or the wolf ate the lamb.

A. Mary did loss her lamb and the wolf eat the lamb.
B. Mary did loss her lamb and the wolf did not eat the lamb.
C. Mary did not loss her lamb and the wolf did not eat the lamb.
D. None
Answer» C. Mary did not loss her lamb and the wolf did not eat the lamb.
100.

## Write the negation in good english sentence : I will not win the game or I will not enter the contest.

A. I will not win the game and I will enter the contest.
B. I will win the game and I will enter the contest.
C. I will win the game and I will not enter the contest.
D. None
Answer» B. I will win the game and I will enter the contest.